Pre-orders for reasoning about stability properties with respect to input of hybrid systems

10 years 3 hour ago

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rs on systems are the basis for abstraction based veriﬁcation of systems. In this paper, we investigate preorders for reasoning about stability with respect to inputs of hybrid systems. First, we present a superposition type theorem which gives a characterization of the classical incremental input-to-state stability of continuous systems in terms of the traditional ✏- deﬁnition of stability. We use this as the basis for deﬁning a notion of incremental inputto-state stability of hybrid systems. Next, we present a preorder on hybrid systems which preserves incremental inputto-state stability, by extending the classical deﬁnitions of bisimulation relations on systems with input, with uniform continuity constraints. We show that the uniform continuity is a necessary requirement by exhibiting counter-examples to show that weaker notions of input bisimulation with just continuity requirements do not su ce to preserve stability. Finally, we demonstrate that the deﬁnitions are use...

Pavithra Prabhakar, Jun Liu, Richard M. Murray

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